Equalizer for AM in-band on-channel radio receivers that does not require analog signal bandwidth information

ABSTRACT

A method is provided for equalizing OFDM symbol vectors received on AM in-band on-channel radio signal including a main carrier and first and second BPSK modulated subcarriers. The method comprises: computing a BPSK magnitude signal; filtering the BPSK magnitude signal; filtering complex samples received on the main carrier; using the filtered BPSK magnitude signal and the filtered complex samples received on the main carrier to compute a plurality of flat fade equalization coefficients; and multiplying the OFDM symbol vectors by the flat fade equalization coefficients. A receiver that includes an equalizer, which operates in accordance with the method is also provided.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a divisional application of U.S. patent applicationSer. No. 12/710,534, filed Feb. 23, 2010, which is a divisionalapplication of U.S. patent application Ser. No. 11/272,978, filed Nov.14, 2005. Both of these applications are hereby incorporated byreference.

FIELD OF THE INVENTION

This invention relates to radio broadcasting and, more particularly tomethods of, and apparatus for, equalizing a signal in a receiver for usein an in-band on-channel digital broadcasting system.

BACKGROUND OF THE INVENTION

An AM compatible in-band on-channel (IBOC) digital broadcasting systemsimultaneously broadcasts analog and digital signals in a standard AMbroadcasting channel. One AM IBOC system is described in U.S. Pat. No.5,588,022. The broadcast signal includes an amplitude modulated radiofrequency signal having a first frequency spectrum. The amplitudemodulated radio frequency signal includes a first carrier modulated byan analog program signal. The signal also includes a plurality ofdigitally modulated carrier signals within a bandwidth, whichencompasses the first frequency spectrum. Each of the digitallymodulated carrier signals is modulated by a digital signal. A firstgroup of the digitally modulated carrier signals lies within the firstfrequency spectrum and is modulated in quadrature with the first carriersignal. Second and third groups of the digitally modulated carriersignals lie outside of the first frequency spectrum and are modulatedboth in-phase and in quadrature with the first carrier signal. Thesubcarriers are divided into primary, secondary and tertiary partitions.Some of the subcarriers are complementary subcarriers.

The received multi-carrier signal requires equalization in the presenceof dynamic channel response variations. Without such equalization, adistorted signal would be detected and the digital broadcasting signalinformation would be unrecoverable. An equalizer enhances therecoverability of the digital audio broadcasting signal information.Equalizers for use in receivers that receive AM in-band on-channelsignals are disclosed in U.S. Pat. Nos. 5,559,830; 6,292,511; 6,295,317;and 6,480,536.

The use of complementary subcarriers for hybrid secondary and tertiarypartitions in the AM compatible digital audio broadcasting signalcreates an orthogonal relationship with the analog host signal. Priorequalization implementations for secondary partitions required knowledgeof whether the analog host bandwidth was limited to ±5 kHz. If theanalog was limited to ±5 kHz, then the secondary partitions wereequalized independently to better accommodate adjacent channelinterference. Otherwise the secondary partitions were firstcomplementary combined to cancel the analog signal in this region.

There is a need for an equalization technique that does not requireanalog bandwidth information.

SUMMARY OF THE INVENTION

This invention provides a method for equalizing OFDM symbol vectorsreceived on AM in-band on-channel radio signal including a main carrierand first and second BPSK modulated subcarriers. The method comprises:computing a BPSK magnitude signal; filtering the BPSK magnitude signal;filtering complex samples received on the main carrier; using thefiltered BPSK magnitude signal and the filtered complex samples receivedon the main carrier to compute a plurality of flat fade equalizationcoefficients; and multiplying the OFDM symbol vectors by the flat fadeequalization coefficients.

Receivers that include equalizers, which operate in accordance with theabove method, are also provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a spectral diagram of the AM hybrid IBOC signal.

FIG. 2 is a spectral diagram of the AM all-digital IBOC signal.

FIG. 3 is a functional block diagram of an AM IBOC receiver.

FIG. 4 is a block diagram of a modem for an AM IBOC receiver.

FIG. 5 is a block diagram of a flat fade equalizer constructed inaccordance with the invention.

FIG. 6 is a block diagram of a partition equalizer constructed inaccordance with the invention.

DETAILED DESCRIPTION OF THE INVENTION

Referring to the drawings, FIG. 1 is a spectral diagram of an AM hybridIBOC signal. The AM hybrid IBOC waveform 10 includes the conventional AManalog signal 12 (bandlimited to about ±5 kHz) along with a nearly 30kHz wide digital audio broadcasting (DAB) signal 14 transmitted beneaththe AM signal. The spectrum is contained within a channel 16 having abandwidth of about 30 kHz. The channel is divided into a centralfrequency band 18, and upper 20 and lower 22 frequency bands. Thecentral frequency band is about 10 kHz wide and encompasses frequencieslying within about ±5 kHz of the center frequency f_(o) of the channel.The upper sideband extends from about +5 kHz from the center frequencyto about +15 kHz from the center frequency. The lower sideband extendsfrom about −5 kHz from the center frequency to about −15 kHz from thecenter frequency.

AM hybrid IBOC DAB signal format in one embodiment of the inventioncomprises the analog modulated carrier signal 24 plus 162 OFDMsubcarrier locations spaced at approximately 181.7 Hz, spanning thecentral frequency band and the upper and lower sidebands. Coded digitalinformation, representative of the audio or data signals (programmaterial), is transmitted on the subcarriers. The symbol rate is lessthan the subcarrier spacing due to a guard time between symbols.

As shown in FIG. 1, the upper sideband is divided into a primarypartition 26 and a secondary partition 28, and the lower sideband isdivided into a primary partition 30 and a secondary partition 32. Thedigital signals are transmitted in the primary and secondary partitionson either side of the host analog signal, as well as underneath the hostanalog signal in a tertiary partition 34. The tertiary partition 34 canbe considered to include a plurality of groups of subcarriers labeled36, 38, 40 and 42 in FIG. 1. Subcarriers within the tertiary partitionthat are positioned near the center of the channel are referred to asinner subcarriers and subcarriers within the tertiary partition that arepositioned farther from the center of the channel are referred to asouter subcarriers. In this example, the power level of the innersubcarriers in groups 38 and 40 is shown to decrease linearly withfrequency spacing from the center frequency. The remaining groups ofsubcarriers 36 and 42 in the tertiary sideband have substantiallyconstant power levels.

FIG. 1 also shows two reference subcarriers 44 and 46, for systemcontrol, that are positioned at the first subcarrier positionsimmediately adjacent to the analog modulated carrier and have powerlevels which are fixed at a value that is different from the othersidebands.

The center carrier 24, at frequency f_(o), is not QAM modulated, butcarries the main analog amplitude modulated carrier. The synchronizationand control subcarriers 44 and 46 are modulated in quadrature to thecarrier. The remaining subcarriers of the tertiary partition, positionedat locations designated as 2 through 26 and −2 through −26 on eitherside of the AM carrier, are modulated with QPSK. Representativesubcarrier locations are identified by the subcarrier index shown inFIG. 1. Subcarriers at locations 2 through 26 and −2 through −26 oneither side of the central frequency, are referred to as tertiarysubcarriers and are transmitted in complementary pairs such that themodulated resultant DAB signal is in quadrature to the analog modulatedAM signal. The use of complementary subcarrier pairs in an AM IBOC DABsystem is shown in U.S. Pat. No. 5,859,876. The synchronization andcontrol subcarriers 44 and 46 are also modulated as a complementarypair.

The double sideband (DSB) analog AM signal occupies the bandwidth in the±15 kHz region. The lower and upper tertiary partitions occupy sub-bandsfrom about 0 to about −5 kHz and from about 0 to about +5 kHz regions,respectively. These tertiary partitions are negative complex conjugatesof each other and are characterized as complementary. This complementaryproperty maintains an orthogonal relationship between the analog anddigital tertiary signals such that they can be separated in a receiver,while existing conventional receivers can still receive the analog AMsignal. The tertiary partitions must be complementary combined toextract the digital signal while canceling the analog crosstalk. Thesecondary partitions also have the complementary property, so they canbe processed at the receiver either independently, or aftercomplementary combining, depending on interference conditions and audiobandwidth. The primary partitions are transmitted independently.

FIG. 2 is a spectral diagram of an all-digital IBOC signal 50. The powerof the central frequency band 52 subcarriers is increased, relative tothe hybrid format of FIG. 1. Again, the two subcarriers 54 and 56located at locations −1 and +1 use binary phase shift keying to transmittiming information. A core upper sideband 58 is comprised of carriers atlocations 2 through 26, and a core lower sideband 60 is comprised ofsubcarriers at locations −2 through −26. Sidebands 58 and 60 formprimary partitions. Two groups 62 and 64 of additional enhancementsubcarriers occupy locations 27 through 54 and −54 through −27respectively. Group 62 forms a secondary partition and group 64 forms atertiary partition. The all-digital format of FIG. 2 is very similar tothe hybrid format except that the AM signal is replaced with a delayedand digitally encoded tuning and backup version of the program material.The central frequency band occupies approximately the same spectrallocation in both the hybrid and all-digital formats. In the all-digitalformat, there are two options for transmitting the main version of theprogram material in combination with the tuning and backup version. Theall-digital system has been designed to be constrained within ±10 kHz ofthe channel central frequency, f_(o), where the main audio informationis transmitted within ±15 kHz of f_(o), and the less important audioinformation is transmitted in the wings of the channel mask out to ±10kHz at a lower power level. This format allows for graceful degradationof the signal while increasing coverage area. The all-digital systemcarries a digital time diversity tuning and backup channel within the ±5kHz protected region (assuming the digital audio compression is capableof delivering both the main and audio backup signal within the protected±5 kHz). The modulation characteristics of the all-digital system arebased upon the AM IBOC hybrid system.

The all-digital IBOC signal includes a pair of primary partitions in the±5 kHz region, a secondary partition in the −5 kHz to −10 kHz region,and a tertiary partition in the +5 kHz to +10 kHz region. Theall-digital signal has no analog component, and all partitions aretransmitted independently (that is, the partitions are notcomplementary).

FIG. 3 is a functional block diagram of an IBOC receiver 84 constructedin accordance with this invention. The IBOC signal is received onantenna 86. A bandpass preselect filter 88 passes the frequency band ofinterest, including the desired signal at frequency f_(c), but rejectsthe image signal at f_(c)−2f_(if) (for a low side lobe injection localoscillator). Low noise amplifier 90 amplifies the signal. The amplifiedsignal is mixed in mixer 92 with a local oscillator signal f_(lo)supplied on line 94 by a tunable local oscillator 96. This creates sum(f_(c)+f_(lo)) and difference (fc−f_(lo)) signals on line 98.Intermediate frequency filter 100 passes the intermediate frequencysignal f_(if) and attenuates frequencies outside of the bandwidth of themodulated signal of interest. An analog-to-digital converter 102operates using a clock signal f_(s) to produce digital samples on line104 at a rate f_(s). Digital down converter 106 frequency shifts,filters and decimates the signal to produce lower sample rate in-phaseand quadrature signals on lines 108 and 110. A digital signal processorbased demodulator 112 then provides additional signal processing toproduce an output signal on line 114 for output device 116.

The receiver in FIG. 3 includes a modem constructed in accordance withthis invention. FIG. 4 is a functional block diagram of an AM HD Radio™modem 130 showing the functional location of the carrier tracking ofthis invention. An input signal on line 132 from the digital downconverter is subject to carrier tracking and automatic gain control asshown in block 134. The resulting signal on line 136 is subjected to asymbol tracking algorithm 138 that produces the BPSK signal on lines 140and 142, symbol vectors (in the time domain) on line 144, and the analogmodulated carrier on line 146. BPSK processing, as shown in block 148produces block/frame sync and mode control information 150 that is usedby functions illustrated in other blocks. An OFDM demodulator 152demodulates the time domain symbol vectors to produce frequency domainsymbol vectors on line 154.

The equalizer 156 processes the frequency domain symbol vectors incombination with the BPSK and carrier signals to produce equalizedsignals on line 158 and channel state information on line 160. Thesesignals are processed to produce branch metrics 162, deinterleaved in adeinterleaver 164, and mapped in a deframer 166 to produce soft decisionbits on line 168. A Viterbi decoder 170 processes the soft decision bitsto produce decoded program data units on line 172.

For clarity, we differentiate the OFDM vectors as time domain andfrequency domain vectors, each representing the same information. Themodem processes these OFDM vectors in the following order (referring toFIG. 4): Carrier Tracking, Symbol Tracking, OFDM Demodulation & BPSKprocessing, and then Equalization. The input to the modem comprises timedomain vectors, or just a sequence of time samples; the Carrier Trackingoperates in the time domain. The Symbol Tracking operates on the timedomain samples and outputs (symbol synchronized) time domain OFDMvectors, and also computes the middle 3 FFT bins (0,±1) representing themain carrier and BPSK subcarriers in the frequency domain. The maincarrier and the BPSK subcarriers are used for the equalization and areconveniently received from the symbol tracking, although they could alsobe received from the OFDM demodulation function (windowed FFT) havingthe same redundant 3 middle FFT bins. The Equalizer always operates onthe sequence of frequency domain OFDM vectors.

This invention relates to a method and apparatus for equalizing eitherthe hybrid or all-digital AM IBOC signals. The equalizer is comprised oftwo cascaded components, a flat fade equalizer followed by a partitionequalizer with noise variance estimates used subsequently in thegeneration of channel state information (CSI). Flat fade compensation isapplied in a similar manner to both the hybrid and all-digital signals.The partition equalizer operates on each of the partitions of thereceived signal. In one example, each partition consists of a set of 25OFDM subcarriers, spanning approximately 5 kHz per partition. Thepartitions of the all-digital IBOC signal comprise a pair of primarypartitions, a secondary partition and a tertiary partition, and areequalized independently. However the secondary and tertiary partitionsof the hybrid signal involve additional processing and combiningtechniques described below. Several other single subcarriers are alsotransmitted between the partitions and use a simpler equalizationtechnique than described here.

The flat fade compensation (equalizer) is described next. The flat fadecompensation involves phase compensation using the main carrier phase,and magnitude equalization using the imaginary components of the BPSKsignal. This flat fade compensation should be applied to all OFDMsubcarriers.

Consider a single digital QAM (complex) symbol (Q(n,1)=x+j·y), and ananalog signal component (a(n,1)=u+j·v) of an AM IBOC signal. This symbolis one of a group of QAM symbols transmitted in the n^(th) OFDM symbolat subcarrier frequency f_(c). The QAM symbol is transmitted using acomplementary subcarrier pair to avoid AM crosstalk.s(t)=[a(n,1)+Q(n,1)]·w(t)·e ^(j·2·π·f) _(c)^(·t)+[a(n,−1)+Q(n,−1)]·w(t)·e ^(−j·2·π·f) _(c) ^(·t) whereQ(n,−1)=−Q*(n,1) and a(n,−1)=a*(n,1).

The receiver demodulates the signal, which has been added to the analogmodulation component and is further corrupted by noise and phase error,to produce the following estimates of the symbols for the pair ofsubcarriers:D(n,1)=∫(s(t)+n(t))·w(t)e ^(−j·2·π·f) ^(c) ^(·t+j·φ) ·dt=Q(n,1)·e ^(j·φ)+a(n,1)·e ^(j·φ) +n ₁D(n,−1)=∫(s(t)+n(t))·w(t)e ^(−j·2·π·f) ^(c) ^(·t+j·φ) ·dt=Q(n,−1)·e^(j·φ) +a(n,−1)·e ^(j·φ) +n ⁻¹.

To show the effect of the complementary combining, the analog componentcan be extracted by summing the two components. The analog signal can bereproduced using the real part of the result, or, more commonly,computing its magnitude.

$\begin{matrix}{\frac{{D( {n,1} )} + {D^{*}( {n,{- 1}} )}}{2} = \frac{{{Q( {n,1} )} \cdot {\mathbb{e}}^{j \cdot \phi}} + {{a( {n,1} )} \cdot {\mathbb{e}}^{j \cdot \phi}} + n_{1} - {{Q( {n,1} )} \cdot {\mathbb{e}}^{{- j} \cdot \phi}} + {a{( {n,1} ) \cdot {\mathbb{e}}^{{- j} \cdot \phi}}} + n_{- 1}^{*}}{2}} \\{= {{{- j} \cdot {Q( {n,1} )} \cdot {\sin(\phi)}} + {{a( {n,1} )} \cdot {\cos(\phi)}} + n_{c} + {j \cdot n_{s}}}} \\{{\cong {a( {n,1} )}};{{when}\mspace{14mu}\phi\mspace{14mu}{and}\mspace{14mu}{noise}\mspace{14mu}{are}\mspace{14mu}{sufficiently}\mspace{14mu}{{small}.}}}\end{matrix}$

The digital symbol is extracted as

$\begin{matrix}{\frac{{D( {n,1} )} - {D^{*}( {n,{- 1}} )}}{2} = \frac{{{Q( {n,1} )} \cdot {\mathbb{e}}^{j \cdot \phi}} + {{a( {n,1} )} \cdot {\mathbb{e}}^{j \cdot \phi}} + n_{1} + {{Q( {n,1} )} \cdot {\mathbb{e}}^{{- j} \cdot \phi}} - {{a( {n,1} )} \cdot {\mathbb{e}}^{{- j} \cdot \phi}} - n_{- 1}^{*}}{2}} \\{= {{{Q( {n,1} )} \cdot {\cos(\phi)}} - {j \cdot {a( {n,1} )} \cdot {\sin(\phi)}} + n_{c} + {j \cdot n_{s}}}} \\{{\cong {Q( {n,1} )}};{{when}\mspace{14mu}\phi\mspace{14mu}{and}\mspace{14mu}{noise}\mspace{14mu}{are}\mspace{14mu}{sufficiently}\mspace{14mu}{{small}.}}}\end{matrix}$

The BPSK sequence is transmitted on the first pair of OFDM subcarrierson either side of the main carrier. These BPSK subcarriers aretransmitted at a gain of G_(BPSK), relative to the main carrier at alevel of 1. So each BPSK symbol can be recovered and scaled with thefollowing expression:

$\begin{matrix}{{B(n)} = \frac{{D( {n,1} )} - {D^{*}( {n,1} )}}{2 \cdot G_{BPSK}}} \\{= \frac{{( {x + {j \cdot y}} ) \cdot {\cos(\phi)}} - {j \cdot {a( {n,1} )} \cdot {\sin(\phi)}} + n_{c} + {j \cdot n_{s}}}{G_{BPSK}}} \\{{\cong \frac{x + {j \cdot y}}{G_{BPSK}}};{{when}\mspace{14mu}\phi\mspace{14mu}{and}\mspace{14mu}{noise}\mspace{14mu}{are}\mspace{14mu}{sufficiently}\mspace{14mu}{{small}.}}}\end{matrix}$

However, we are interested in an estimate of the absolute value of theBPSK bit (real scalar) for subsequent scaling of the signal. For thisparticular BPSK symbol, where Q(n,1)=x+j·y, we arbitrarily choose x=0,and the information bit is imposed in the imaginary dimension. Toextract the scalar information R(n) from B(n), either its magnitude canbe computed, or the absolute value of the imaginary component y can beextracted from B(n).R(n)=|B(n)|, or R(n)=abs[Im{B(n)}].

The magnitude estimate is generally less accurate than the absolutevalue of the imaginary computation when the phase error is small. Themagnitude is also more computationally complex, so we choose to avoidthe magnitude computation in favor of the imaginary componentcomputation. The estimate of the channel magnitude R(n) can be computedfrom B(n), or more directly from D(n,1) and D*(n,−1).

$\begin{matrix}{{R(n)} = {{abs}\lbrack {{Im}\{ {B(n)} \}} \rbrack}} \\{= \frac{{abs}\lbrack {{{Im}\{ {D( {n,1} )} \}} - {{Im}\{ {D^{*}( {n,{- 1}} )} \}}} \rbrack}{2 \cdot G_{BPSK}}} \\{= {\frac{{abs}\lbrack {{{Im}\{ {D( {n,1} )} \}} + {{Im}\{ {D( {n,{- 1}} )} \}}} \rbrack}{2 \cdot G_{BPSK}}.}}\end{matrix}$Notice that R(n) is a real-valued scalar.

A functional block diagram of the flat fade equalizer 180 is presentedin FIG. 5. An input D(n) from the OFDM demodulator is supplied on line182. In this embodiment, the input is a 256-sample vector for eachsymbol n. R(n) is computed as shown in block 184 and passed to a medianfilter 186 to produce a first filtered signal on line 188. The firstfiltered signal is further filtered by a finite impulse response filter190 to produce a second filtered signal on line 192.

In this embodiment, the filtering for the BPSK magnitude signal R(n)includes a 7-tap median filter cascaded with a 7-tap FIR filter. Thismedian filter can be implemented by placing the samples of R(n) in a7-element circular buffer, then computing the median of the 7 samples.The median filter has a delay of 3 samples. The 7-tap FIR filter has adelay of 3 samples and can be implemented using the following 7coefficients:

${h(k)} = {( {\frac{1}{16}\frac{2}{16}\frac{3}{16}\frac{4}{16}\frac{3}{16}\frac{2}{16}\frac{1}{16}} ).}$

The total delay of the median and FIR filters is 6 samples. The filteredchannel magnitude can be expressed as

${{\overset{\sim}{R}( {n - 6} )} = {\sum\limits_{k = 0}^{6}\;{{h(k)} \cdot \{ {{median}\lbrack {R( {n - k} )} \rbrack} \}}}};$where the median is computed over 7 samples.

The main carrier phase is also corrected as a flat fade component.However, this phase should be filtered independently of the previousBPSK magnitude. This is due to the increased phase noise on carriersamples near pinchoff at the negative analog modulation peaks. The sameFIR filtering 194 defined for the BPSK magnitude can be used for themain carrier phase, although the median filtering should not be used,but replaced with an equivalent delay 196 to match the delay of themagnitude component. The main carrier samples C(n) can be computedindependently over each OFDM symbol, or the value computed in the OFDMdemodulation can be used. The filtering of the main carrier component isas follows:

${\overset{\sim}{C}( {n - 3} )} = {\sum\limits_{k = 0}^{6}\;{{h(k)} \cdot {{C( {n - k} )}.}}}$

The flat fade equalizer weight is the reciprocal of the filtered channelmagnitude (with divide by zero protection, ε), while applying theconjugate of the main carrier phase, after an appropriate delay,

$W_{ff} = \frac{{\overset{\sim}{C}}^{*}( {n - 6} )}{{\max\lbrack {{\overset{\sim}{R}( {n - 6} )},ɛ} \rbrack} \cdot {{\overset{\sim}{C}( {n - 6} )}}}$as shown in block 198.

The original input is delayed as shown in block 200 and multiplied byW_(ff) as shown in multiplier 202 to produce an output 256-sample vectorfor each new symbol n−6 after flat fade equalization on line 204.

The algorithm for computing the flat fade equalization coefficientW_(ff) for each new OFDM symbol is summarized next:

“Flat Fade Equalization algorithm”${{R(n)} = {{{abs}\lbrack {{Im}\{ {B(n)} \}} \rbrack} = \frac{{abs}\lbrack {{{Im}\{ {D( {n,1} )} \}} + {{Im}\{ {D( {n,{- 1}} )} \}}} \rbrack}{2 \cdot G_{BPSK}}}};\begin{matrix}{{compute}\mspace{14mu}{BPSK}\mspace{14mu}{signal}\mspace{14mu}{amplitude}} \\{{{nominal}\mspace{14mu} R(n)} = 1}\end{matrix}$${{{\overset{\sim}{R}( {n - 6} )} = {\sum\limits_{k = 0}^{6}\;{{h(k)} \cdot \{ {{median}\lbrack {R( {n - k} )} \rbrack} \}}}};{{{filtered}\mspace{14mu} 7} - {{sample}\mspace{14mu}{median}}}},{{delay} = {6\mspace{14mu}{symbols}}}$${{{\overset{\sim}{C}( {n - 3} )} = {\sum\limits_{k = 0}^{6}\;{{h(k)} \cdot {C( {n - k} )}}}};{{filtered}\mspace{14mu}{the}\mspace{14mu}{main}\mspace{14mu}{carrier}\mspace{14mu}{samples}\mspace{14mu}({complex})}},{{delay} = {3\mspace{14mu}{symbols}}}$${W_{ff} = \frac{{\overset{\sim}{C}}^{*}( {n - 6} )}{{\max\lbrack {{\overset{\sim}{R}( {n - 6} )},ɛ} \rbrack} \cdot {{\overset{\sim}{C}( {n - 6} )}}}};\begin{matrix}{{compute}\mspace{20mu}{flat}\mspace{20mu}{fade}\mspace{20mu}{coefficient}\mspace{20mu}{for}\mspace{20mu}{multiplication}} \\{{{with}\mspace{20mu}{OFDM}\mspace{20mu}{symbol}\mspace{20mu}{subcarriers}},{{delay} = {6\mspace{20mu}{{symbols}.}}}}\end{matrix}$

Filtering for the BPSK magnitude signal R(n) includes a 7-tap medianfilter cascaded with a 7-tap FIR filter.

The flat fade equalization described above is followed by the Partitionequalization. Table 1 shows the locations of interleaved symbols(indices), including training symbols “T” within each partition block.Each column represents a partition.

TABLE 1

Next, an algorithm is used to compute the equalizer coefficients andassociated noise variances estimated for each of the 25 elements(columns for subcarriers) of each OFDM symbol within a partition (forexample, the upper primary partition). The equalizer begins processingOFDM symbols as they are received. All partitions of the all-digitalmodes and the primary partitions of the hybrid mode are processedindependently for each OFDM symbol containing 25 columns (perpartition). The hybrid secondary partitions are processed independently,and after complementary combining, allowing selection of the maximummetric, depending upon whether the analog audio bandwidth is limited to5 kHz. The hybrid tertiary partitions are processed only aftercomplementary combining.

Each column of a partition contains either 1 or 2 training symbols(complex), depending upon which of the 16 rows is processed. Thetraining symbol locations repeat every 16 OFDM symbols (rows). Thelocations of the training symbols are conveniently computed as afunction of the particular row (modulo 16) of the OFDM symbol. Therecent training symbols are next collected in a 25-column vector TS,simply updating the column(s) of TS(col) corresponding to the recentcolumn(s) of the OFDM symbol containing the training symbol. The mediansand variances of adjacent groups of symbols are computed after theadjacent group is updated with recent training symbols. Next thevariances and medians are filtered using a two-dimensional recursivefilter technique. The equalizer coefficients are computed from thefiltered medians and equalization is applied to all the correspondingcolumns for the previous OFDM symbol, along with the updated noisevariances (and reciprocals) for subsequent symbol processing. Thedetails of this process are described next and presented in FIG. 6.

FIG. 6 is a functional block diagram of an equalizer that can be usedfor each 25-column partition. The OFDM symbol OFDM(r,col) is input online 210. Training symbols are collected as shown in block 212. Themedians and variances are computed as shown in block 214 to producemedian and variance signals on line 216. These signals are filtered andequalized in block 218 to produce an equalized variance signal on line220 (for use in subsequent channel state information (CSI) estimates)and equalization coefficients on line 222. After a delay as shown inblock 224, the equalization coefficients are applied to the input signalas shown in block 226 to produce an output signal on line 228.

To compute the medians and variances from the training symbols (TS),first, create two, 1-row by 25-column matrices labeled TS and MED to beused to store the training symbols and median computations,respectively. The column indices (col=0 to 24) equal the correspondingcolumns of the training symbols as they are received for each OFDMsymbol. Next, initialize the elements to zero.

Then, receive the next OFDM symbol row r (modulo 16) corresponding to aparticular row (r) of an interleaver block. Identify the training symbollocation(s), or column(s), for this row r, and place the trainingsymbol(s) into corresponding TS(col). The training symbol in a row r canbe updated using the following algorithm.

The partition equalizer performs several steps.

Step 1: Gather, collapse and update the Training Symbols into aconvenient vector TS (representing the timely training symbolinformation) used in subsequent equalization processing.

-   -   “Algorithm to update TS for row r”    -   col=mod(3·r+1, 16); “identify which column has new TS”    -   TS(col)=OFDM(r,col)    -   if col<9 then TS(col+16)=OFDM(r, col+16); “if second TS in this        row”.

Step 2: Create two, 25-column vectors labeled MED and logVAR to be usedto store the computed median and log of the variance values forequalization and CSI. Median filtering of the local (time & freq) TSsamples is used to produce a median value estimate of the TS. Theoutputs Med & logVAR are local estimates (not yet time or frequency(across subcarriers) smoothed) of these parameters.

The column indices equal the corresponding columns of the trainingsymbols as they are received for each OFDM symbol. Then initialize theelements to zero.

Compute median and variance for the TS(col) 6 rows after that particularTS(col) was updated. This delay ensures that its adjacent trainingsymbols are also updated for use in the following computation. Either 1or 2 TS(col) values are updated for each new row r. A 9-sample medianand variance are computed for columns 4 through 20 using ±4 values oneither side of this training symbol. For example, the median computationfor column 4 uses training symbols TS(0) through TS(8). Columns 0through 3, and 21 through 24 are special cases since fewer than 9samples are available at the ends to compute the median and variancevalues. The extreme missing values are replaced with duplicate values byfolding near the ends, when necessary. For example in computing themedian for column 3, TS(0) through TS(7) are used, and the missingTS(−1) column is replaced with TS(0) to provide 9 values for the mediancomputation. The computed median and variance values are placed inMED(col) and logVAR(col). The following method (pseudocode) can be usedto identify the appropriate columns to update at this row r, and gatherthe appropriate TS samples for the 9-sample median and log variancecomputations:

“Algorithm to update MED and log VAR vectors, delay = 6 symbols” col =mod(3 · r + 15, 16) ; “identify first TS col for r − 6” FOR m = 0 to 8 ;“gather 9 adjacent TS to place in buffer for MED & logVAR computation”  colm = col + m − 4    ${TScolindx} = \{ \begin{matrix}{{{- 1} - {colm}};} & {{{if}\mspace{14mu}{colm}} < 0} \\{{colm};} & {otherwise}\end{matrix} $   TSmedbuff (m) = TS(TScolindx) MED(col) =median(TSmedbuff) ; “complex median, separate real & imaginary” “computelog base2 of VAR samples (vector)”${{logVAR}({col})} = {\log\; 2( {\max\lbrack {\frac{1}{256},{\min\lbrack {256,{\frac{1}{8} \cdot {\sum\limits_{m = 0}^{8}\;{{{{MED}({col})} - {{TSmedbuff}(m)}}}^{2}}}} \rbrack}} \rbrack} )}$if col < 9 then ; “update second TS in this row if exists - - - ”  col2= col + 16  FOR m = 0 to 8   colm = col2 + m − 4   ${TScolindx} = \{ \begin{matrix}{{49 - {colm}};} & {{{if}\mspace{14mu}{colm}} > 24} \\{{colm};} & {otherwise}\end{matrix} $   TSmedbuff (m) = TS(TScolindx)  MED(col2) =median(TSmedbuff) ; “complex median, separate real & imaginary”  ${{logVAR}( {{col}\; 2} )} = {\log\; 2( {\max\lbrack {\frac{1}{256},{\min\lbrack {256,{\frac{1}{8} \cdot {\sum\limits_{m = 0}^{8}\;{{{{MED}( {{col}\; 2} )} - {{TSmedbuff}(m)}}}^{2}}}} \rbrack}} \rbrack} )}$end if.

To compute the equalizer coefficients and channel state information(CSI), the next step is to smooth (filter) the median and variancevalues over time and frequency (columns). The log of the variance isused for smoothing the squared noise samples having a potentially largedynamic range over the subcarriers.

Create two, 25-column vectors labeled MED1 and logVAR1 to be used tostore the recursive time-filtered median and log variance values,respectively. The column indices equal the corresponding columns of thetraining symbols as they are received for each OFDM symbol. Theninitialize the elements to zero.

Create two, 25-column vectors labeled MED2 and logVAR2 to be used tostore the column or frequency-filtered median and log variance values,respectively. The column indices equal the corresponding columns of thetraining symbols as they are received for each OFDM symbol. Theninitialize the elements to zero.

The equalizer values EQ are computed from MED2. The EQ values aregenerally the complex reciprocal of MED2 values, but with divideprotection. The variance values logVAR2 are used to compute VAREQ forsubsequent CSI and branch metrics after adjustment for equalizer gains.

Step 3: Next smooth the MED and logVAR values over time and frequency(subcarriers). The time smoothing with the IIR filter results in MED1 &logVAR1. The frequency smoothing using one of the quadratic fitfunctions results in MED2 & logVAR2. See first part of algorithmdescribed below.

Step 4: The equalizer values EQ are computed from MED2. The EQ valuesare generally the complex reciprocal of MED2 values, but with divideprotection. The variance values logVAR2 are used to compute VAREQ forsubsequent CSI and branch metrics after adjustment for equalizer gains.Note that the last line of the algorithm above computes VAREQ(col) in amanner that accommodates special conditions. It is not simply theantilog computation to convert logVAR (log of the variance estimate) toVAR. It accounts for the fact that the variance is computed onnot-yet-equalized values, so an adjustment is made to be compatible withthe equalized symbol values of the output. Further adjustment is made toavoid variance estimate errors when very high interference is present.Both of these adjustments are included in the factormax[Eqmagsq(col,max(Eqmagsq)/2] after the antilog.

“Algorithm to compute EQ & VAREQ from MED & logVAR, filter delay = 16symbols” “IIR filter MED and logVAR each col to get MED1 and logVAR1, q= 1/8 IIR coef” MED1 = (1 − q) · MED1 + q · MED ; logVAR1 = (1 − q) ·logVAR1 + q · logVAR ; “Smooth MED1 and logVAR1 across cols usingquadratic - fit interpolator” “MED2 & logVAR2 are the freq - smoothedmedian and variance estimates” MED2 = QF (MED1) ; “compute quadratic fitusing QF algorithm” logVAR2 = QF(logVAR1) ; “compute quadratic fit usingQF algorithm” “Compute equalizer coefficients EQ from MED2” medsq(col) =|MED2(col)|² ; col = 0 . . . 24 “save squared magnitudes”${{{EQ}({col})} = \frac{{MED}\; 2^{*}{({col}) \cdot T}}{\max\lbrack {{{medsq}({col})},10^{- 6}} \rbrack}};\begin{matrix}{{col} = {0\mspace{14mu}\ldots\mspace{14mu} 24}} \\{``{{{equalizer}\mspace{14mu}{coeffs}},{T = {{Training}\mspace{14mu}{{sym}.}}}}"}\end{matrix}$ “Compute antilog and equalize logVAR2 to produce VAREQ”EQmagsq(col) = |EQ(col)|² ; col = 0 . . . 24VAREQ(col) = 2^(logVAR 2(col)) ⋅ max [EQmagsq(col), max (EQmagsq)/2]; col = 0  …  24.

The EQ(col) values are then applied to the corresponding data-bearingsymbols to produce OFDMEQ(col) values for each column of the OFDM symbol(delayed by 22 OFDM symbols to account for the EQ processing delay). TheVAREQ(col) values are used for subsequent CSI processing.OFDMEQ(col)=OFDM(col)·EQ(col); col=0 . . . 24 “equalize delayed OFDMsymbol.

The algorithm described above uses a function called QF, which is aquadratic fit of the MED1 or logVAR1 matrices used to smooth the valuesacross the columns (subcarriers) of these matrices. The smoothing ofthese values reduces the estimation and correction errors due to noisesince the variation needing equalization is assumed to be smooth. Thevariation of these values across the columns can be a result of severalfactors. One factor is due to a residual symbol tracking timing errorcausing a linear phase shift across the subcarriers. Since the filteringis done in the I and Q complex domain, and not phase and magnitude, theI and Q components resulting from this linear phase shift cannot becorrected exactly with a linear fit, but rather a quadratic fit for Iand Q complex components provides sufficient accuracy. Another variationcan be due to the phase and amplitude perturbations due to frequencyselective fading over the subcarriers, which can also be corrected bythe quadratic fit. Phase and amplitude ripple from analog filteringprior to OFDM demodulation can be corrected if the ripple is small.Interference also tends to have a shape for logVAR that can beaccommodated with a quadratic fit.

If the analog filter ripple is severe and deviates from a quadraticshape, then a different QF function is needed. Therefore two algorithmoptions are presented: the first QF function is best for correcting thevariations due to residual symbol timing error, selective channelfading, and mild filter ripple; the second algorithm is designed tocorrect all these variations plus a more severe filter ripple.

The first QF function estimates three points over the subcarriers towhich a quadratic shape is fitted to perform the smoothing correction.These points are estimated using FIR filters at the middle and twoextreme endpoints of the subcarrier span. The middle point is properlyestimated using a symmetric FIR filter over the middle subcarrier. TheFIR filters at the endpoints have a centroid that is several bins fromthe ends. Although the quadratic fit could be normally designed to usethe proper centroids near the endpoints and extrapolate the remainingsubcarriers at the extreme ends, the performance tends to be better ifthe centroids are assumed to be located at the extreme subcarrierlocations. The reason is that the extrapolation tends to accentuate thecurvature of the quadratic fit in the presence of noise. However thealgorithm can be modified to place the centroids at the location thatyields the best overall performance.

Step 4a: The first quadratic fit function is intended to smooth theestimates with a partition shape (assumed quadratic) that providesnear-optimum smoothing given likely channel conditions such astime-offset and selective fading properties. This is accomplished usingthe following algorithm.

“QF(x), Quadratic Fit function, input vector x, output vector y. (25 -element vectors)${{{wf}(k)} = \frac{{\cos( \frac{\pi \cdot k}{12} )} + 1}{13}};{{{for}\mspace{14mu} k} = {0\mspace{14mu}\ldots\mspace{14mu} 11}};{{stored}\mspace{14mu}{coeffs}\mspace{14mu}{for}\mspace{14mu}{filter}\mspace{14mu}{points}}$${{ylow} = {\sum\limits_{k = 0}^{11}\;{{{wf}(k)} \cdot {x(k)}}}};{``{{output}\mspace{20mu}{value}\mspace{20mu}{at}\mspace{20mu}{col}\mspace{20mu} 0}"}$${{yhigh} = {\sum\limits_{k = 0}^{11}\;{{{wf}(k)} \cdot {x( {24 - k} )}}}};{``{{output}\mspace{20mu}{value}\mspace{20mu}{at}\mspace{20mu}{col}\mspace{20mu} 24}"}$${{ymid} = {{\frac{1}{12} \cdot {\sum\limits_{k = 0}^{24}\;{x(k)}}} - {\frac{13}{24} \cdot ( {{ylow} + {yhigh}} )}}};{``{{midpoint}\mspace{20mu}{value}\mspace{20mu}{at}\mspace{20mu}{col}\mspace{20mu} 12}"}$${a = \frac{{ylow} + {yhigh} - {2 \cdot {ymid}}}{288}};{``{{quadratic}\mspace{20mu}{coef}\mspace{20mu} a}"}$${b = \frac{{4 \cdot {ymid}} - {3 \cdot {ylow}} - {yhigh}}{24}};{``{{quadratic}\mspace{20mu}{coef}\mspace{20mu} b}"}$y(col) = a · col² + b · col + ylow ; col = 0 . . . 24 ; “output vectory”.

An alternate quadratic fit function QF is provided to accommodate IFfilters with excessive ripple and group delay or gain variations. Thisfunction is different from the first since a different quadratic curveis used at each subcarrier location to form the FIR filter coefficients.These quadratic curves are pre-computed and stored in a 25 by 25 matrixW to be used as a multiplier for the row of 25 values from thesubcarriers to be filtered. So instead of computing the quadratic fitacross the 25 subcarriers for each new OFDM symbol as in the firstalgorithm, the second algorithm simply multiplies the vector of 25subcarrier values by the matrix W for each OFDM symbol time.

This alternate QF function is applied in a similar manner as a methodknown as the Savitsky-Golay (SG) procedure; however, the alternate QFfunction generates the coefficients in a different manner resulting inimproved filtering gain against noise while solving the endpointdilemma. The SG procedure computes a least-squares fit centered on eachpoint to smooth the data for that point. The result is a set of FIRfilter coefficients about each subcarrier location to be smoothed. Twofactors motivate the use of least squares smoothing. One is thevariability of the values over the subcarriers, and the other is theendpoint dilemma where the subcarriers near the endpoints cannot befitted with a symmetric set of FIR filter coefficients since there areno subcarriers to use in the filtering beyond the endpoints. The SGprocedure exploits the properties of manipulated Vandermonde matrices togenerate the FIR coefficients, generating a unique set of FIR filtercoefficients for each subcarrier location to be smoothed. Although theSG procedure produces FIR filter coefficients that result in an unbiasedestimate of each smoothed subcarrier value, the actual set of FIRcoefficients do not have the best noise reduction filtering propertiesdue to the excessive use of negative coefficient values. However, thealternate QF function uses the best possible quadratic fit FIRcoefficients for noise reduction filtering or smoothing, whilepreserving the zero bias property of the SG procedure. Furthermore, thealternate QF function has more flexibility in establishing the span ofFIR filter smoothing about the subcarrier locations.

One example of the alternate QF function is described as follows. Thespan of the nonzero FIR filter coefficients for each subcarrier locationis set to 15 nonzero coefficients to accommodate the anticipatedvariability of values across the 25 subcarriers in the partition,although this can be adjusted. The unique FIR filter coefficients foreach of the subcarrier locations m=0 . . . 24 are computed. The shape ofthe FIR coefficients is a quadratic function with four additionalconstraints defined as follows:

Constraint 1: The number of nonzero FIR filter coefficients is 15, with10 zero coefficients remaining. The center nonzero coefficient isnormally located on the subcarrier to be smoothed resulting in asymmetric FIR filter property, except that the 7 subcarriers on eitherend are constrained by using the 15 subcarrier locations on that end forthe nonzero coefficients. Then the first nonzero coefficient location pfor estimating (filtering) the subcarrier m can be identified byp=max(0,min(17,m−7)); “p is the first nonzero coefficient location”.

Constraint 2: Each set of the 25 sets of 25 FIR coefficients, having 15nonzero coefficients and 10 zero coefficients, must sum to unity so thateach FIR filter has a dc gain of one for each subcarrier location.

${{\sum\limits_{k = 0}^{24}\;{{FIR}( {m,k} )}} = 1};$for the kth coefficient estimating the mth subcarrier.

Constraint 3: The centroid of the FIR filter for subcarrier m must alsobe m to ensure an unbiased estimate when the slope of the subcarrierdata is assumed to be piecewise linear.

${\sum\limits_{k = 0}^{24}\;{k \cdot {{FIR}( {m,k} )}}} = {m.}$

Constraint 4: Although the best noise reduction can be achieved byminimizing the sums of the squares of the coefficients, this does notprovide the best local estimate for each subcarrier location, and wouldresult in 15 linear coefficients for each FIR filter. A betterconstraint is to ensure that the quadratic function crosses zero at theunused coefficient locations just outside the 15 nonzero coefficients.This is possible for the 11 subcarrier locations 7 through 17, but thisconstraint cannot be met for the other subcarrier locations affected bythe endpoint dilemma. Then the outer subcarrier locations have the zerocrossing constraint only toward the inner point beyond the FIRcoefficient span.y _(m)(k)=a _(m) ·k ² +b _(m) ·k+c _(m); “quadratic for the kth coef forthe mth subcarrier”y _(m)(p−1)=0; “constraint for m=7 . . . 24”y _(m)(p+15)=0; “constraint for m=0 . . . 17”.

Constraint 1 simply establishes the range of the 15 nonzero coefficientsfor each of the 25 FIR filters having a quadratic characteristic overthat range. Constraints 2, 3 and 4 constitute the three equationsnecessary to determine the quadratic coefficients a_(m), b_(m) and c_(m)for each FIR filter. Although Constraint 4 may seem to overdetermine themiddle sets of filter coefficients for m=7 . . . 17, having zeroendpoints at both ends, this double constraint for these subcarriers isredundant, and all sets of coefficients are properly determined. Analgorithm for generating the alternate QF1(x) FIR filter coefficientmatrix W is defined next, and the resulting coefficient values for W arepresented as shown below.

Step 4b: An alternate quadratic fit function QF is provided toaccommodate IF filters with excessive ripple and group delay or gainvariations. This function is different from the first since a differentquadratic curve is used at each subcarrier location to form the FIRfilter coefficients. These quadratic curves are pre-computed and storedin a 25 by 25 matrix W to be used as a multiplier for the row of 25values from the subcarriers to be filtered. So instead of computing thequadratic fit across the 25 subcarriers for each new OFDM symbol as inthe first algorithm, the second algorithm simply multiplies the vectorof 25 subcarrier values by the matrix W for each OFDM symbol time. Theseare subjected to constraints 1-4, which result in the followingalgorithm.

“QF1(x), Alternate Quadratic Fit Matrix function, input row vector x,output vector y.” “first compute prestored coefficient matrix W (25 by25)” FOR m = 0 to 7   ${a(m)} = \frac{14 - {3 \cdot m}}{4760}$  ${b(m)} = \frac{1 + {2360 \cdot {a(m)}}}{120}$  c(m) = −225 · a(m) − 15· b(m)  FOR k = 0 to 14   W(k, m) = a(m) · k² + b(m) · k + c(m)   W(24 −k, 24 − m) = W(k, m) FOR m = 8 to 16  FOR k = 0 to 14   W(k + m − 7, m)= W(k, 7) “This is the end of the prestored computation for filtermatrix W” “compute filtered output vector y for each new OFDM symbol” y= x · W ; “matrix multiply yields output vector y”.

Step 4c: A third alternative quadratic fit is described below.

Another alternate filter QF2(x) can be designed using all 25 possiblenonzero coefficients for each FIR filter. This filter has acharacteristic more similar to the first QF(x) filter, but isconstructed in the matrix form W of the alternate filter.

“QF2(x), Alternate Quadratic Fit Matrix function, input row vector x,output vector y.” “first compute prestored coefficient matrix W (25 by25)” FOR m = 0 to 13   ${a(m)} = {\frac{2}{2925} - \frac{m}{11700}}$  ${b(m)} = {\frac{- 1}{39} + \frac{11 \cdot m}{3900}}$  ${c(m)} = {\frac{25}{117} - \frac{2 \cdot m}{117}}$  FOR k = 0 to 24  W(k, m) = a(m) · k² + b(m) · k + c(m)   W(24 − k, 24 − m) = W(k, m)“This is the end of the prestored computation for filter matrix W”“compute filtered output vector y for each new OFDM symbol” y = x · W ;“matrix multiply yields output row vector y”.

In another aspect, the invention involves the adaptive complementarycombining of the secondary partitions before equalization. The twoindependent secondary partitions are equalized independently, along withthe associated VAREQ estimates. The branch metrics are computedindependently and redundantly for all secondary soft code bits in thepartition. The corresponding branch metrics are then added to produceone set of branch metrics. The equalization is also performed on thecomplementary combined secondary partitions to produce another set ofbranch metrics for the same set of secondary soft code bits. Then foreach secondary soft code bit, the higher branch metric is selected asoutput for the corresponding secondary soft code bits.

The use of complementary subcarriers for hybrid secondary and tertiarypartitions creates an orthogonal relationship with its analog host. Aprior implementation of the secondary equalization required knowledge ofwhether the analog host bandwidth was limited to ±5 kHz. If the analogwas limited to ±5 kHz, then the secondary partitions were equalizedindependently to better accommodate adjacent channel interference.Otherwise the secondary partitions were first complementary combined tocancel the analog signal in this region.

The input symbols to be equalized are delayed, to match the delay in theestimation of the equalizer parameters to provide timely application ofthe equalizer information. The EQ(col) values are then applied to thecorresponding data-bearing symbols to produce OFDMEQ(col) values foreach column of the OFDM symbol (delayed by 22 OFDM symbols to accountfor the EQ processing delay). The VAREQ(col) values are used forsubsequent CSI processing.

The method of this invention does not make use of the analog bandwidthinformation; instead both independent and combined equalizations areperformed, and later the maximum branch metric is selected. This yieldsmore robust performance, especially when the analog bandwidth somewhatexceeds 5 kHz.

The tertiary subcarriers are always complementary combined prior toequalization. Tertiary equalization is then performed as described. Thetwo secondary partitions are processed both independently andcomplementary combined, yielding three sets of equalized branch metricsfor the single set of secondary soft code bits. The method of combiningthese three sets of branch metrics is described next.

The two independent secondary partitions are equalized independently,along with the associated VAREQ estimates. The branch metrics arecomputed independently and redundantly for all secondary soft code bitsin the partition. The corresponding branch metrics are then added toproduce one set of branch metrics. The equalization is also performed onthe complementary combined secondary partitions to produce another setof branch metrics for the same set of secondary soft code bits. Then foreach secondary soft code bit, the higher branch metric is selected asoutput for the corresponding secondary soft code bits.

As described above, the equalizer includes two parts: a flat fadecompensation (equalizer) followed by a partition equalizer. The flatfade equalizer helps in fast fading cases and uses the main carrier (FFTbin 0) and BPSK subcarriers (bins ±1). The partition equalizer is slowerand operates on sparser training symbols in the partition, but is moreaccurate in the partition. The partition equalizer benefits from theflat fade equalizer to keep the training values in a relative smallerrange.

The functions shown in the drawings can be implemented using knowncircuit components, including but not limited to, one or more processorsor application specific integrated circuits.

While the invention has been described in terms of several examples, itwill be apparent to those skilled in the art that various changes can bemade to the described examples without departing from the scope of theinvention as set forth in the following claims.

What is claimed is:
 1. A method of equalizing OFDM symbol vectorsreceived on an AM in-band on-channel radio signal including a maincarrier and first and second BPSK modulated subcarriers, the methodcomprising: using a processor to compute a BPSK magnitude signal;filtering the BPSK magnitude signal; filtering complex samples receivedon the main carrier; using the filtered BPSK magnitude signal and thefiltered complex samples received on the main carrier to compute aplurality of flat fade equalization coefficients; and multiplying theOFDM symbol vectors by the flat fade equalization coefficients.
 2. Themethod of claim 1, wherein the step of filtering the BPSK magnitudesignal comprises: passing the BPSK magnitude signal through a medianfilter and a finite impulse response filter.
 3. The method of claim 1,wherein the step of filtering complex samples received on the maincarrier comprises: passing the complex samples received on the maincarrier through a finite impulse response filter.
 4. The method of claim1, wherein the step of computing a BPSK magnitude signal comprises:extracting an absolute value of an imaginary component of a BPSK symbol.5. The method of claim 1, wherein the first and second BPSK modulatedsubcarriers are modulated in quadrature to the main carrier.
 6. Themethod of claim 1, wherein the first and second BPSK modulatedsubcarriers are modulated as a complementary pair of subcarriers.
 7. Themethod of claim 1, wherein the step of multiplying the OFDM symbolvectors by the flat fade equalization coefficients produces flat fadeequalized OFDM symbol vectors, and the method further comprises:computing a plurality of partition equalization coefficients; andmultiplying the flat fade equalized OFDM symbol vectors by the partitionequalization coefficients to produce output OFDM symbol vectors.
 8. Areceiver for receiving an AM in-band on-channel radio signal including amain carrier and first and second BPSK modulated subcarriers, thereceiver comprising: an input for receiving the AM in-band on-channelradio signal; an equalizer for computing a BPSK magnitude signal, forfiltering the BPSK magnitude signal, for filtering complex samplesreceived on the main carrier, for using the filtered BPSK magnitudesignal and the filtered complex samples received on the main carrier tocompute a plurality of flat fade equalization coefficients, and formultiplying the OFDM symbol vectors by the flat fade equalizationcoefficients; and an output device for producing an output in responseto the AM in-band on-channel radio signal.
 9. The receiver of claim 8,wherein the equalizer comprises: a median filter and a finite impulseresponse filter for filtering the BPSK magnitude signal.
 10. Thereceiver of claim 8, wherein the equalizer comprises: a finite impulseresponse filter for filtering the complex samples received on the maincarrier.
 11. The receiver of claim 8, wherein the equalizer computes theBPSK magnitude signal by extracting an absolute value of an imaginarycomponent of a BPSK symbol.
 12. The receiver of claim 8, furthercomprising; a partition equalizer for computing a plurality of partitionequalization coefficients, and multiplying the flat fade equalized OFDMsymbol vectors by the partition equalization coefficients to produceoutput OFDM symbol vectors.